Glissement intermateriaux lors de simulations ALE en grandes déformations et grandes vitesses

National audienceLors de simulations de milieux multimatériaux en grandes déformations avec une méthode ALE, l'interface entre les matériaux peut se retrouver à l'intérieur des mailles de calcul. Il faut donc mettre en place une stratégie spécifique dans ces mailles mixtes. La méthode proposée, basée sur les éléments finis enrichis permet d'avoir un champ de vitesse propre à chaque matériau y compris dans les mailles mixtes. La réunion des différents champs de vitesse peut présenter une discontinuité sur l'interface ce qui donne la liberté nécessaire à la simulation du glissement entre les matériaux.See http://hal.archives-ouvertes.fr/docs/00/59/27/08/ANNEX/r_MF58LJ0L.pd

Modélisations multi-matériaux multi-vitesses en dynamique rapide

Many simulations in fluid structure interactions, multiphase flows or dynamic impacts involve independent structures interacting through complex interfaces. For such problems, standard strategies often use a Lagrangian approach using one finite element mesh per structure and adequate matching strategies. These are very demanding in mesh generation, and are difficult to use in presence of large mesh distortions. An alternative is to use an Eulerian strategy describing the different structures on a single grid using a single average velocity field and developing ad hoc constitutive laws to handle the multiphase microstructure of each element. These models are usually quite crude on the interface physics. In this context, there is a renewed interest in models which will use a single global smooth mesh, not matching the structures and independent finite element velocity fields to describe the motion of the structures. This strategy is attractive but faces difficult challenges: interface tracking, development of adequate ALE formulations because materials and mesh velocities are different, proper treatment of the kinematic continuity constraints between the structures. Great care must be taken at this level in order to propose a stable approach which is locking free and stays robust in large strain elastodynamics. With this thesis, we propose an original strategy based on an enriched finite element method. It defines one FE velocity field by material on a single mesh, the different fields are overlapping and form an enriched field that can have a discontinuity at the interface and allows to describe sliding between the materials. The discontinuity is controlled by a normal velocity constraint at the interface and an additional unknown of interface pressure that is the Lagrange multiplier associated with the constraint. The ALE formulation used is based on a time split between Lagrangian phase and remap phase. The Lagrangian phase is solved by the Wilkins explicit scheme widely used while the remap is done by mesh intersections between Lagrangian meshes deformed by material and a smoothed average mesh. The interface is tracked during the remap by the volume fraction of each material in the cells and it reconstruction can be discontinuous across elements. Two variants of the methods are introduced, analysed and compared. They differ by their Lagrange multiplier discretization and consequently by their velocity constraint discretization: -the node continuity uses a Lagrange multiplier defined at nodes. This variant is simple and fast but does not take correctly into account the compressibility of materials, -the cell continuity uses a Lagrange multiplier constant by interface segment. This variant gives better results than the first one. The method is stabilized by adding internal nodes in the mixed cells using piecewise linear velocity shape functions inside each element and a proper mass lumping ensures a stable equilibration of the interface. The internal node momentum equation is discretized by an implicit scheme. The consequence is that a system coupling the interface nodes has to be solved in order to compute the velocities near the interface. The two variants have been implemented into an industrial code. They are validated and compared with several test cases involving different situations like fluid-structure interaction or sliding between solids.De nombreuses simulations dans les domaines des impacts, des interactions fluide-structure ou des écoulements multiphasiques impliquent différentes structures indépendantes interagissant entre elles à travers des interfaces complexes. Pour ces problèmes, les stratégies classiques utilisent souvent une approche lagrangienne utilisant un maillage éléments finis par structure et des stratégies de couplage et de mise en contact adéquates. Ceci est très coûteux en terme de génération de maillages et difficile à mettre en place en présence de grandes déformations. Une alternative est d'utiliser une stratégie " eulérienne " décrivant les différentes structures sur une grille unique en utilisant une vitesse moyenne unique et en développant des lois d'état ad hoc pour gérer le caractère multiphasique des éléments traversés par l'interface. La physique de l'interface de ces modèles est en générale assez grossière. Dans ce contexte, il y a un regain d'intérêt pour les modèles utilisant un maillage global unique non conforme avec les structures et définissant des champs de vitesses éléments finis indépendants pour décrire le mouvement de chacune des structures. Cette stratégie est intéressante mais induit différents problèmes : suivi d'interface, développement d'une formulation ALE adaptée car les matériaux et le maillage ont des vitesses différentes, traitement correct de la contrainte cinématique à l'interface entre les structures. Une grande attention doit être portée à ce dernier point pour proposer une approche stable, sans verrouillage numérique et restant robuste en cas de grandes déformations. Dans cette thèse, nous proposons une stratégie originale basée sur une méthode d'éléments finis enrichis. Elle définit un champ de vitesse éléments finis par matériau sur un unique maillage. Les différents champs se recouvrent et forment un champ enrichi qui peut avoir une discontinuité à l'interface et permet de décrire le glissement entre les matériaux. La discontinuité est contrôlée par une contrainte de continuité des vitesses normales et par une inconnue supplémentaire, la pression d'interface qui est le multiplicateur de Lagrange associé à la contrainte cinématique. La formulation ALE utilisée est basée sur une décomposition du pas de temps entre phase lagrangienne et phase de projection. La phase lagrangienne est résolue par le schéma de Wilkins classique des codes hydrodynamiques alors que la projection est réalisée par calcul d'intersection entre les maillages lagrangiens déformés par la matière et un maillage commun plus régulier. L'interface est construite à partir de la fraction volumique de chaque matériau et sa reconstruction peut être discontinue entre les éléments. Deux variantes sont introduites, analysées et comparées. Elles diffèrent par la discrétisation du multiplicateur de Lagrange et donc, par celle de la contrainte de vitesse : -la continuité par nœud utilise un multiplicateur défini aux nœuds. Cette variante est simple et rapide mais ne prend pas correctement en compte les différences de compressibilité entre matériaux, -la continuité par maille utilise un multiplicateur constant par segment d'interface. Cette variante donne des résultats meilleurs que la première version. La méthode est stabilisée par l'ajout de nœuds internes dans les mailles mixtes dont les fonctions bulles associés sont linéaires par morceaux dans chaque élément ainsi que par une condensation de la masse adaptée pour assurer un équilibre stable de l'interface. L'équation de mouvement du nœud interne est discrétisée par un schéma implicite en temps. En conséquence, nous devons résoudre un système couplant tous les nœuds de l'interface pour calculer les vitesses autour de l'interface. Les deux variantes ont été implantées dans un code industriel. Elles sont validées et comparées dans plusieurs cas tests impliquant diverses situations comme des interactions fluide-structure ou du glissement entre solides

Modélisations multi-matériaux multi-vitesses en dynamique rapide

PALAISEAU-Polytechnique (914772301) / SudocSudocFranceF

Modelling complex high speed multimaterial evolutions using a single mesh multivelocity strategy

International audienceIn the present paper, we propose another space discretization of the kinematic constraint for a single grid multi velocity formulation leading to a better approximation of the interface physics. The paper is organized as follows. In the next section, we will briefly review the problem to solve and the single mesh multi-velocity discretization strategy. In Section 3, we will then introduce our new cell-based discretization of the normal velocity continuity constraint on the interface, develop the proper velocity enrichment, and analyse its stability. A generic time discretization is next introduced in Section 4 and adapted to the specific space discretization proposed herein. The proposed methodology is finally validated on a few numerical examples

New adaptative static condensation method for the simulation of large dimensions prestressed reinforced concrete structures

International audienceIn order to evaluate the cracking process in large reinforced and prestressed concrete structures, a predictive model of concrete damage with refined mesh and a nonlinear law can be required. Because of the computational load, such modelling is not applicable directly on large-scale structures whose characteristic dimensions are over several meters. To solve this problem, a method based on the static condensation, which concentrates the computational effort on the damaged area has been proposed. The so-called “zones of interest” are evolutionary to be adapted to the cracking process. The method has been developed, improved and implemented in the finite element code Cast3m. It follows different steps including an initial cutting of the mesh into sub-zones, a condensation of these zones on their borders and the definition of the first “zone of interest” by a preliminary linear computation. The borders of « non-risky » zones are then condensed at the interface of this initial zone of interest (“double condensation”). The nonlinear computation is finally applied only on the zone(s) of interest, consequently reducing the computational load. At the end of each calculation time, a potential evolution of the zones of interest is considered through either criteria of “propagation” or “apparition” (evolving method). In this contribution, the “adaptive condensation method” is presented and the influence of the input parameters is discussed. Among them, the initial decomposition of the mesh into sub-zones plays a key role in the efficiency of the method. In order to improve the initial method, an automatic division procedure is proposed to enhance the initial mesh cutting. It is especially shown how this procedure, based on a limited number of parameters, can significantly decrease both the user effort and the computational time. The method is finally applied on test cases of different complexity: a 2D three-point bending beam, a simplified reinforced concrete containment and a prestressed beam. Both global and local results are compared to “reference” simulation using classical finite element methods. Similar results are obtained, even for very local quantities (damage), with a variable calculation time saving factor ranging from 4 to 15 for the case of the prestressed beam

Application of the Adaptive Static Condensation Method on the Vercors Mock-Up

In order to evaluate the cracking phenomenon in large reinforced and prestressed concrete structures, a predictive simulation of concrete damage with a fine mesh and a nonlinear law is necessary. Due to the computational cost, such modeling is not applicable to the scale of the complete structure. To solve this difficulty, a method called “Adaptive Static Condensation: ASC” was initially proposed in (Llau et al., 2015) then developed in (Mezher et al., 2022). It is based on static condensation (Guyan, 1965), and aims to concentrate the effort on the damaged area. In this contribution, the applicability and efficiency of ASC are shown on the 1/3 scale mock-up of a containment vessel (Vercors). The ASC allow to reach levels of simulations inaccessible in complete calculation while using a non-local model of damage for the concrete

Achieving Higher Levels of Crack Simulation with the Improved Adaptive Static Condensation Method

International audienceAccurately simulating concrete cracking in large-dimensional structures is a challengingtask. To address this issue, an adaptive static condensation (ASC) method has been developed that has demonstrated effectiveness in localized nonlinearities. The ASC method aims to concentrate computational efforts solely on the damaged area, which may evolve due to crack initiation or propagation. However, the efficiency of the ASC method may be limited as it is based on a nonevolving mesh. To overcome this limitation, a novel approach is proposed in this study, which utilizes an evolutionary mesh with mesh refinement. The proposed approach employs a fine mesh solely in the activated and evolving domain of interest. The ASC method with mesh refinement isdemonstrated on a notched bending beam, indicating that the accuracy of the ASC is maintained while providing an additional gain in computational time. Furthermore, a reinforced concrete vessel subjected to internal pressure is considered, and it is shown that this new approach results in a significant improvement in computational time, with a 14-fold improvement compared to a 5-fold improvement without mesh refinement. This study demonstrates that the proposed improvement on the ASC method allows for finer discretization in the zones of interest that were previously inaccessible with the nominal ASC method or a direct numerical simulation strategy

Simulation of large dimensional reinforced and prestressed concrete structures using a new adaptive static condensation method including automatic mesh partitioning

International audienceIn order to evaluate the cracking process in large reinforced and pre-stressed concrete structures, a predictive simulation of concrete damage with a refined mesh and a nonlinear law is required. Because of the computational load, such modelling is not applicable directly on large-scale structures whose characteristic dimensions are over several tens of meters. To deal with this type of structure, an adaptive static condensation method (ASC), which concentrates the computational effort on the damaged area (domain of interest) only, is proposed. The ASC method is first presented. A particular attention is paid to the needed developments to extend its domain of application up to prestressed concrete structures. The method is then applied to a three point bending prestressed beam and validated by comparison to a classical finite element damage computation. The numerical efficiency of the proposed approach is evaluated with, on this application, a time saving factor of about 15.An automatic mesh partitioning method is then implemented to make the method even more efficient. Based on physical considerations, it takes into account the expected shape and the evolution of the damaged regions during the loading. It is applied to three test cases with different geometries and loading to discuss the calibration process through a sensitivity analysis. A unique set of parameters is finally proposed and the efficiency of the method is demonstrated. As a conclusion; a complete automatic method is made available for the simulation of large scale reinforced and prestressed concrete structure

Intégration du principe de raffinement de maillage dans la méthode de Condensation Statique Adaptative (ASC)

International audienceAfin d'évaluer le phénomène de fissuration dans les grandes structures en béton armé et précontraint, un modèle prédictif de l'endommagement du béton avec un maillage raffiné et une loi de comportement non linéaire peut être requis. En raison du cout de calcul, une telle modélisation est difficilement applicable à l’échelle de la structure complète. Pour résoudre cette difficulté, une méthode basée sur la condensation statique, qui concentre l'effort de calcul sur la zone endommagée, a été proposée. Dans ce travail, la méthode a été développée en y intégrant le principe de raffinement automatique du domaine d'intérêt (DI)

MANTA : un code HPC généraliste pour la simulation de problèmes complexes en mécanique

International audienceLe code MANTA a l’ambition de permettre la réalisation de simulations complexes en mécanique sur des supercalculateurs actuels et futurs tout en préservant les fondamentaux des codes développés au CEA : adaptabilité au problème posé, robustesse des algorithmes, pérennité des modèles et du code. On expose les principes de développement de ce code de nouvelle génération, et quelques exemples représentatifs de ses capacités actuelles sont également décrits